Relation Disjoint

• Defined in ontology: Kif-sets
• Source pathname: /tmp_mnt/vol/q/htw/cms/ontolingua/examples/kif/../../all-ontologies/kif/kif-sets.lisp

Instance-Of@Frame-Ontology: Binary-Relation@Ol-User%Kif-Relations, Relation@Ol-User%Kif-Relations, Set

Arity@Frame-Ontology: 2

Documentation@Ol%Frame-Ontology:

Two sets are disjoint if and only if there is no object that is a member of both sets.

Notes:

• Source: KIF Version 3.0 Specification

Equivalence Axioms for Disjoint:

(<=> (Disjoint ?S1 ?S2) (Empty (Intersection ?S1 ?S2)))

Equivalence Axioms mentioning Disjoint:

(<=> (Pairwise-Disjoint @Sets)
     (Forall (?S1 ?S2)
             (=> (Item@Ol-User%Kif-Lists ?S1 (Listof @Sets))
                 (Item@Ol-User%Kif-Lists ?S2 (Listof @Sets))
                 (Or (= ?S1 ?S2) (Disjoint ?S1 ?S2)))))

Axioms mentioning Disjoint:

(Forall (?S)
        (=> (Not (Empty ?S))
            (Exists (?U) (And (Member ?U ?S) (Disjoint ?U ?S)))))